.TH  SGBEQUB 1 "November 2008" "    LAPACK routine (version 3.2)                                 " "    LAPACK routine (version 3.2)                                 " 
.SH NAME
SGBEQUB - computes row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number
.SH SYNOPSIS
.TP 20
SUBROUTINE SGBEQUB(
M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
AMAX, INFO )
.TP 20
.ti +4
IMPLICIT
NONE
.TP 20
.ti +4
INTEGER
INFO, KL, KU, LDAB, M, N
.TP 20
.ti +4
REAL
AMAX, COLCND, ROWCND
.TP 20
.ti +4
REAL
AB( LDAB, * ), C( * ), R( * )
.SH PURPOSE
SGBEQUB computes row and column scalings intended to equilibrate an
M-by-N matrix A and reduce its condition number.  R returns the row
scale factors and C the column scale factors, chosen to try to make
the largest element in each row and column of the matrix B with
elements B(i,j)=R(i)*A(i,j)*C(j) have an absolute value of at most
the radix.
.br
R(i) and C(j) are restricted to be a power of the radix between
SMLNUM = smallest safe number and BIGNUM = largest safe number.  Use
of these scaling factors is not guaranteed to reduce the condition
number of A but works well in practice.
.br
This routine differs from SGEEQU by restricting the scaling factors
to a power of the radix.  Baring over- and underflow, scaling by
these factors introduces no additional rounding errors.  However, the
scaled entries\(aq magnitured are no longer approximately 1 but lie
between sqrt(radix) and 1/sqrt(radix).
.br
.SH ARGUMENTS
.TP 8
M       (input) INTEGER
The number of rows of the matrix A.  M >= 0.
.TP 8
N       (input) INTEGER
The number of columns of the matrix A.  N >= 0.
.TP 8
KL      (input) INTEGER
The number of subdiagonals within the band of A.  KL >= 0.
.TP 8
KU      (input) INTEGER
The number of superdiagonals within the band of A.  KU >= 0.
.TP 8
AB      (input) DOUBLE PRECISION array, dimension (LDAB,N)
On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
The j-th column of A is stored in the j-th column of the
array AB as follows:
AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
.TP 8
LDAB    (input) INTEGER
The leading dimension of the array A.  LDAB >= max(1,M).
.TP 8
R       (output) REAL array, dimension (M)
If INFO = 0 or INFO > M, R contains the row scale factors
for A.
.TP 8
C       (output) REAL array, dimension (N)
If INFO = 0,  C contains the column scale factors for A.
.TP 8
ROWCND  (output) REAL
If INFO = 0 or INFO > M, ROWCND contains the ratio of the
smallest R(i) to the largest R(i).  If ROWCND >= 0.1 and
AMAX is neither too large nor too small, it is not worth
scaling by R.
.TP 8
COLCND  (output) REAL
If INFO = 0, COLCND contains the ratio of the smallest
C(i) to the largest C(i).  If COLCND >= 0.1, it is not
worth scaling by C.
.TP 8
AMAX    (output) REAL
Absolute value of largest matrix element.  If AMAX is very
close to overflow or very close to underflow, the matrix
should be scaled.
.TP 8
INFO    (output) INTEGER
= 0:  successful exit
.br
< 0:  if INFO = -i, the i-th argument had an illegal value
.br
> 0:  if INFO = i,  and i is
.br
<= M:  the i-th row of A is exactly zero
.br
>  M:  the (i-M)-th column of A is exactly zero
